Correct answer: 3. 
The given chemical reaction is between ammonium fluoride and magnesium chloride to form magnesium fluoride and ammonium chloride.
The balanced chemical equation representing the reaction will be,
The complete ionic equation for the reaction: All the compounds soluble in water (aqueous) will split into ions, 
will not split into ions as it is insoluble in water.
The net ionic equation will be:
Here the spectator ions are 
Answer:
70%
Explanation:
To find the percent yield, you need to (1) convert grams HCl to moles (via molar mass from periodic table), then (2) convert moles HCl to moles H₂ (via mole-to-mole ratio from equation), then (3) calculate the percent yield H₂ (via percent yield equation).
Zn (s) + 2 HCl (aq) --> ZnCl₂ (aq) + 1 H₂ (g)
Molar Mass (HCl): 1.008 g/mole + 35.45 g/mole
Molar Mass (HCl) = 36.458 g/mole
125 g HCl 1 mole HCl 1 mole H₂
--------------- x ------------------ x ------------------ = 1.7 moles H₂
36.458 g 2 moles HCl
(actual yield / theoretical yield) x 100% = percent yield
theoretical/calculated yield = 1.7 moles H₂
actual yield = 1.2 moles H₂
(1.2 moles H₂ / 1.7 moles H₂) x 100% = 71%
Therefore, the best percent yield of hydrogen produced is 70%.
<span>Exactly 4(4 - 2*2^(1/3) + 2^(2/3)) feet,
or approximately 12.27023581 feet.
Let's first create an equation to calculate the relative intensity of the light based upon the distance D from the brighter light source. The distance from the dimmer light source will of course be (20-D). So the equation will be:
B = 4/D^2 + 1/(20-D)^2
The minimum and maximum can only occur at those points where the slope of the equation is 0. And you can determine the slope by using the first derivative. So let's calculate the first derivative.
B = 4/D^2 + 1/(20-D)^2
B' = d/dD [ 4/D^2 + 1/(20-D)^2 ]
B' = 4 * d/dD [ 1/D^2 ] + d/dD [ 1/(20-D)^2 ]
B' = 4(-2)D^(-3) + (-2)(20 - D)^(-3) * d/dD [ 20-D ]
B' = -8/D^3 - 2( d/dD [ 20 ] - d/dD [ D ] )/(20 - D)^3
B' = -8/D^3 - 2(0 - 1)/(20 - D)^3
B' = 2/(20 - D)^3 - 8/D^3
Now let's find a zero.
B' = 2/(20 - D)^3 - 8/D^3
0 = 2/(20 - D)^3 - 8/D^3
0 = 2D^3/(D^3(20 - D)^3) - 8(20 - D)^3/(D^3(20 - D)^3)
0 = (2D^3 - 8(20 - D)^3)/(D^3(20 - D)^3)
0 = 2D^3 - 8(20 - D)^3
8(20 - D)^3 = 2D^3
4(20 - D)^3 = D^3
4(8000 - 1200D + 60D^2 - D^3) = D^3
32000 - 4800D + 240D^2 - 4D^3 = D^3
32000 - 4800D + 240D^2 - 5D^3 = 0
6400 - 960D + 48D^2 - D^3 = 0
-6400 + 960D - 48D^2 + D^3 = 0
D^3 - 48D^2 + 960D - 6400 = 0
We now have a simple cubic equation that we can use the cubic formulas to solve.
Q = (3*960 - (-48)^2)/9 = 64
R = (9*(-48)*960 - 27*(-6400) - 2*(-48)^3)/54 = -384
D = Q^3 + R^2 = 64^3 + (-384)^2 = 409600
Since the value D is positive, there are 2 imaginary and 1 real root. We're only interested in the real root.
S = cbrt(-384 + sqrt(409600))
S = cbrt(-384 + 640)
S = cbrt(256)
S = 4cbrt(4)
T = cbrt(-384 - sqrt(409600))
T = cbrt(-384 - 640)
T = cbrt(-1024)
T = -8cbrt(2)
The root will be 4cbrt(4) - 8cbrt(2) + 48/3
So simplify
4cbrt(4) - 8cbrt(2) + 48/3
=4cbrt(4) - 8cbrt(2) + 16
=4(cbrt(4) - 2cbrt(2) + 4)
= 4(4 - 2*2^(1/3) + 2^(2/3))
Which is approximately 12.27023581
This result surprises me. I would expect the minimum to happen where the intensity of both light sources match which would be at a distance of 2/3 * 20 = 13.3333 from the brighter light source. Let's verify the calculated value.
Using the brightness equation at the top we have:
B = 4/D^2 + 1/(20-D)^2
Using the calculated value of 12.27023581, we get
B = 4/D^2 + 1/(20-D)^2
B = 4/12.27023581^2 + 1/(20-12.27023581)^2
B = 4/12.27023581^2 + 1/7.72976419^2
B = 4/150.5586868 + 1/59.74925443
B = 0.026567713 + 0.016736611
B = 0.043304324
And the intuition value of 13.33333333
B = 4/D^2 + 1/(20-D)^2
B = 4/13.33333333^2 + 1/(20-13.33333333)^2
B = 4/13.33333333^2 + 1/6.666666667^2
B = 4/177.7777778 + 1/44.44444444
B = 0.0225 +0.0225
B = 0.045
And the calculated value is dimmer. So intuition wasn't correct.
So the object should be placed 4(4 - 2*2^(1/3) + 2^(2/3)) feet from the stronger light source, or approximately 12.27023581 feet.</span>
A tone that is lower in pitch is lower in what characteristic?=frequency
